a$.$ For the two sequences shown below, determine the $N-$point circular convolution of $x_1(n)$ and $x_2(n).$

$x_1(n)=cos(\frac{2}{N}n),x_2(n)=sin(\frac{2}{N}n),0nN-1$

$nd$ IDFT

$($Hint: Use DFT properties and IDFT$)$

b$.$ Prove ${\displaystyle \underset{l=-}{\overset{}{}}}(n+lN)=\frac{1}{N}{\displaystyle \underset{k=0}{\overset{N-1}{}}}{e}^{j(2\frac{}{N})kn}$

$($Hint: Find the DFT of the periodic signal in the left$-$hand side.$)$